Question 25
Let $S$ be a square of side length $1.$ Two points are chosen independently at random on the sides of $S.$ The probability that the straight-line distance between the points is at least $\dfrac{1}{2}$ is $\dfrac{a-b\pi}{c},$ where $a,$ $b,$ and $c$ are positive integers with $\gcd(a,b,c)=1.$ What is $a+b+c?$